Can I move out of state with my children without any formal custody order? NYS ( we are still legally married but separated for years)

Nope. Unless you are looking for a lot of trouble.

NYS is VERY sensitive about such issues. I personally knew a woman who did that, the other spouse raised objections and she was told in no uncertain terms that she would be back in NY with the kids inside of two weeks or the Husband would be granted FULL custody of them.

You can do what you want, but the father has many legal tools to use to bring you back, or at least the kids at your expense, married or NOT.

Agreed, you may move since there is no formal order, but once you move, the father has many options to try and force the children to return to the state. And may file in his state at this time and the time shortly after you move, so all legal actions would be in your current state, not the new state.

Have you spoken to your husband and what was his response ?

Is the other parent an active parent? Would the move prevent the other parent from maintaining the same level of activity. For example, if you lived in the Albany area and moved to the Berkshires this might not cause a hardship. On the other hand if you moved to Virginia it would.

So the answer is not a simple one. There is more information needed.

The bottom line though, is that the other parent has rights. If you move without the other parent's permission then the other parent could file for full custody and the courts would likely order you to turn over custody to the other parent. If you move without informing the other parent and you hide the children from the other parent, then you could be arrested for parental kidnapping.

So I would recommend that you discuss this with the other parent first. If the other parent does not agree to the move, then you need to go to court to get custody and get the court to agree to the move.